1) Evaluate the double integral ∬Dx^2 y dA, where D is the top half of the...

1) Evaluate the double integral ∬Dx^2 y dA, where D is the top half of the disc with center the origin and radius 2 by changing to polar coordinates.

2) Use a double integral to find the area of one loop of the rose r= 6cos (3θ).

3) Use polar coordinates to find the volume of the solid below the paraboloid z=50−2x^2−2y^2 and above the xy-plane.

Expert Solution

For the given region D, we have, In polar coordinates, x=2 cos and y= 2 sin

Where varies from 0 to and r varies from 0 to 2. The step by step explanatory solution is provided below.

milcah answered 2 years ago

using / for integral Evaluate the double integral //R cos( (y-x)/(y+x) )dA where R is the...

using / for integral Evaluate the double integral //R cos( (y-x)/(y+x) )dA where R is the trapezoidal region with vertices (1,0), (2,0), (0,2), and (0,1)

evaluate the integral by making an appropriate change of variables double integral of 5sin(25x^2+64y^2) dA, where...

evaluate the integral by making an appropriate change of variables double integral of 5sin(25x^2+64y^2) dA, where R is the region in the first quadrant bounded by the ellipse 25x^2 +64y^2=1

Calculate the double integral ∫∫Rxcos(x+y)dA∫∫Rxcos⁡(x+y)dA where RR is the region: 0≤x≤π3,0≤y≤π2

Find the double integral of region (2x-y)dA, where region R is in the first quadrant enclosed...

Find the double integral of region (2x-y)dA, where region R is in the first quadrant enclosed by the circle x2+y2=4 and the lines x=0 and y=x

1.) Evaluate the given definite integral. Integral from 4 to 5 dA∫45 (0.2e^−0.2A +3/A) dA 2.)...

1.) Evaluate the given definite integral. Integral from 4 to 5 dA∫45 (0.2e^−0.2A +3/A) dA 2.) Evaluate the definite integral. Integral from negative 1 to 1 dx∫−1 1 (x^2+1) dx 3.) Evaluate the definite integral. Integral from 0 to 2 dx∫02 (2x^2+x+6) dx 4.) Evaluate the definite integral. Integral from 1 to 4 left dx∫14 (x^3/2+x^1/2−x^−1/2) dx 5.) Evaluate the definite integral. Integral from negative 2 to negative 1 dx∫−2−1 (3x^−4) dx

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Use the given transformation to evaluate the integral. (12x + 8y) dA R , where R is the parallelogram with vertices (−1, 3), (1, −3), (2, −2), and (0, 4) ; x = 1/ 4 (u + v), y = 1/ 4 (v − 3u)

Evaluate the integral. (Use C for the constant of integration.) (x^2-1)/(sqrt(25+x^2)*dx Evaluate the integral. (Use C...

Evaluate the integral. (Use C for the constant of integration.) (x^2-1)/(sqrt(25+x^2)*dx Evaluate the integral. (Use C for the constant of integration.) dx/sqrt(9x^2-16)^3 Evaluate the integral. (Use C for the constant of integration.) 3/(x(x+2)(3x-1))*dx

1). Find the dervatives dy/dx and d^2/dx^2 , and evaluate them at t = 2. x...

1). Find the dervatives dy/dx and d^2/dx^2 , and evaluate them at t = 2. x = t^2 , y= t ln t 2) Find the arc length of the curve on the given interval. x = ln t , y = t + 1 , 1 < or equal to t < or equal to 2 3) Find the area of region bounded by the polar curve on the given interval. r = tan theta , pi/6 < or...

1. Evaluate the double integral for the function f(x,y) and the given region R. R is...

1. Evaluate the double integral for the function f(x,y) and the given region R. R is the rectangle defined by -2 x 3 and 1 y e4 2. Evaluate the double integral f(x, y) dA R for the function f(x, y) and the region R. f(x, y) = y x3 + 9 ; R is bounded by the lines x = 1, y = 0, and y = x. 3. Find the average value of the function f(x,y) over the plane region R....

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